POST UTME BOWEN UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality x^2 - 4x - 5 > 0.
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -5 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 5 \) ∪ (1, ∞)
Question 2
Solve the inequality $\frac{x}{x-1} > 0$.
A. $x > 1$
B. $x < 1$
C. $x > 0$
D. $x < 0$
Question 3
Solve the inequality $|x-2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -5 \) \cup \( 1, \infty \)
D. \( -\infty, 5 \) \cup \( 3, \infty \)
Question 4
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \ 0.0 & \text{otherwise} \end{cases} ). Find the expected value of ( X ).
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 5
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 6
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism?
A. 72
B. 96
C. 108
D. 120
Question 7
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 8
Let \( A = egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \) and \( B = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find ( AB ) if it exists.
A. \( egin{bmatrix} 5 & 8 \ 11 & 16 \end{bmatrix} \)
B. \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \)
C. \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \)
D. \( egin{bmatrix} 3 & 5 \ 7 & 11 \end{bmatrix} \)
Question 9
Solve the equation $x^2 + 4x + 4 = 0$.
A. $x = -2$
B. $x = -1$
C. $x = 0$
D. $x = 1$
Question 10
Find the value of $\tan 2\theta$ in terms of $\tan \theta$.
A. $\frac{2\tan \theta}{1-\tan^2 \theta}$
B. $\frac{1-\tan^2 \theta}{2\tan \theta}$
C. $\frac{2\tan \theta}{1+\tan^2 \theta}$
D. $\frac{1+\tan^2 \theta}{2\tan \theta}$
Question 11
Find the area under the curve $y = \frac{1}{x^2+1}$ from $x = 0$ to $x = 1$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 12
Let X be a random variable with probability density function f(x) = \( egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} \). Find the probability that X takes a value greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 13
A rec\tangular box has dimensions 5 cm x 8 cm x 10 cm. Find the volume of the box.
A. 200 cm^3
B. 400 cm^3
C. 600 cm^3
D. 800 cm^3
Question 14
A histogram of exam scores is shown below. If the mean score is 60, what is the median score?
A. 55
B. 60
C. 65
D. 70
Question 15
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.9544
B. 0.8413
C. 0.6915
D. 0.6827

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